Okay, so I have a bit of a tight budget, so I need to choose between the screw autofocus 50mm f/1.8 and the new 35mm f/1.8 DX. I'm not really in a rush, but the 35mm DX is out of stock at my local shop. But, they do have the 50mm. I do have a D40, so focus will be an issue. Is it worth waiting for the 35mm or just getting the 50mm?

It depends on what other lenses and cameras you have.. and what kind of photography you like. On dx the 50mm becomes a specialised portrait and short tele. On FX/film days its the general do everything lens. Nowadays (for FX) its the general do every thing lens when its dark or whne you need real sharp images. Which is what the 35f1.8dx is in the Dx format.

35mm is a little bit boring length at DX, just as 50mm is at FX or 35mm film.
On the other hand 50mm is great on DX (like 75mm is on FX) for portraits for example, and if you get an extension ring or bellows you will get fantastic macro lens also.
But if you are planning to use it on D40 I would not recommend it. D40 viewfinder is quite difficult to use with manual focus lens, and 50mm f/1.8 will be a manual focus lens on D40.
You should better first try manual focusing with the lens you have (turn of AF) and see for yourself if it is OK for you. If it is get 50mm f/1.8. Otherwise get 35mm f/1.8 FX, it is great little lens, and it will autofocus on D40 in a fraction of a second.